Isentropic compression inlet for supersonic aircraft

ABSTRACT

A supersonic inlet employs relaxed isentropic compression to improve net propulsive force by shaping the compression surface of the inlet. Relaxed isentropic compression shaping of the inlet compression surface functions to reduce cowl lip surface angles, thereby improving inlet drag characteristics and interference drag characteristics. Supersonic inlets in accordance with the invention also demonstrate reductions in peak sonic boom overpressure while maintaining performance.

This application claims priority to U.S. Provisional Patent Application60/750,345, filed Dec. 15, 2005, and entitled “Supersonic Inlet Shapedfor Dramatic Reductions in Drag and Sonic Boom Strength,” which ishereby incorporated by reference in its entirety.

FIELD OF THE INVENTION

The embodiments of the invention are related to supersonic inlets forsupersonic aircraft and more particularly to supersonic inlets shaped toreduce drag and sonic boom strength.

BACKGROUND OF THE INVENTION

Many supersonic aircraft employ gas turbine engines that are capable ofpropelling the aircraft at supersonic speeds. These gas turbine engines,however, generally operate on subsonic flow in a range of about Mach 0.3to 0.6 at the upstream face of the engine. The inlet decelerates theincoming airflow to a speed compatible with the requirements of the gasturbine engine. To accomplish this, a supersonic inlet is comprised of acompression surface and corresponding flow path, used to decelerate thesupersonic flow into a strong terminal shock. Downstream of the terminalshock, subsonic flow is further decelerated using a subsonic diffuser toa speed corresponding with requirements of the gas turbine engine.

As is known in the art, the efficiency of the supersonic inlet and thediffusion process is a function of how much total pressure is lost inthe air stream between the entrance side of the inlet and the dischargeside. The total-pressure recovery of an inlet is defined by a ratio oftotal pressure at the discharge to total pressure at freestream.

Supersonic inlets are typically either “2D”, having a rectangularopening, or axisymmetric, having a circular opening. The supersonicinlet includes a throat positioned between a converging supersonicdiffuser and a diverging subsonic diffuser. Supersonic inlets aregenerally also classified into three types: internal compression, mixedcompression, and external compression.

Internal compression inlets accomplish supersonic and subsoniccompression completely within the interior of the inlet duct. Theprimary theoretical advantage of this inlet type is the extremely lowcowling angle that results from a completely internalized shock train.While this inlet design appears theoretically advantageous, in practiceit requires a complex and performance-penalizing shock control system inorder to position the shock train, to “start” the inlet, and to maintaindynamic shock stability to avoid the inlet's high sensitivity to shocktrain expulsion (“unstart”). The challenges associated with this type ofinlet have limited its use to primarily air-breathing missileapplications designed for high Mach number. Below speeds of about Mach3.5, mixed compression and external compression inlets offer a morepractical compromise between performance and complexity.

As the name implies, mixed compression inlets offer a blending ofexternal and internal compression and seek a more practical balancebetween performance and complexity than that offered by fully internalcompression designs in the Mach range from approximately 2.5 to 3.5. Theinternal portion of the shock train of a mixed compression inlet is lesssensitive to flow disturbances than a fully internal design, and haslower cowling angle and drag than a fully external compression inletdesigned to the same speed. But mixed compression nevertheless requiresa complex control system for starting the internal shock train and forstability management to avoid inlet unstart. Two notable applications ofmixed compression include the inlets on the XB-70 Valkyrie and SR-71Blackbird aircraft.

External compression inlets are most appropriate for applications belowabout Mach 2.5. In this speed range, external compression offers adesign simplicity that typically outweighs its generally inferiorpressure recovery. Because the shock train is completely external,cowling angles, and therefore installed drag characteristics, tend to behigher when compared against internal and mixed compression designs atsimilar speed. However, because the shock train on an externalcompression inlet remains completely outside of the internal flow path,it is not subject to the sudden unstart expulsion produced by upstreamor downstream flow disturbances. External compression shock stability istherefore superior to mixed or internal compression designs, requiring asignificantly less complicated inlet control system. Notable examples ofinlets employing external compression include those used on theConcorde, the F-14 Tomcat, and the F-15 Eagle.

Traditional inlet design methods have generally focused on improvingpropulsion system performance by maximizing total inlet pressurerecovery and hence gross engine thrust. Complicated secondary systemsand variable geometry inlets are often used to accomplish this. Whilehigh pressure recovery definitely provides certain gains, maximizingpressure recovery typically comes at the price of significant inlet dragand inlet complexity, characteristics that typically run counter to arobust and low cost-of-operation design.

For example, attempts to increase pressure recovery include bleedair-based methods, which, as is understood in the art, improve inletpressure recovery through shock strength management and boundary layerremoval. The Concorde used a method of bleed air extraction at the inletthroat that weakened the strength of the terminal shock therebyimproving total pressure recovery. However, bleed air-based methodstypically take a large portion of the intake flow to produce the desiredresults and suffer corresponding drag-related penalties once the bleedflow is eventually dumped back overboard. Additionally, extensivesecondary systems are typically required, consisting of complex flowrouting equipment.

Inlet ramp positioning is another method used to improve pressurerecovery through more optimum placement of the compression shock system,particularly at off-design operating conditions. The Concorde, F-14, andF-15 are all examples of aircraft that employ ramp positioning forimproved pressure recovery. However, ramp positioning requires electricor hydraulic actuators and an inlet control system, resulting in a largeincrease in inlet part count and complexity. Such systems introducepotential failure points and add significantly to development andoperating costs.

The traditional supersonic inlet design process begins with theselection of compression surface geometry that best meets theperformance and integration requirements of the intended application,for example aircraft design speed and/or terminal shock Mach number. Foran external compression inlet, a compression surface configurationtypically focuses the inlet-generated shocks, at supersonic designcruise speed, at a location immediately forward of the cowl highlight orcowl lip, generally referred to as shock-on-lip focusing. Thisarrangement generally provides good pressure recovery, low flow spillagedrag, and a predictable post-shock subsonic flow environment that lendsitself to more basic analytical techniques and explains the technique'straceability to the earliest days of supersonic inlet design.

External compression inlet design practice also uses cowl lip angle toalign the cowling lip with the local supersonic flow in the vicinity ofthe terminal shock and the cowl lip. Aligning the lip with the localflow helps to prevent the formation of an adverse subsonic diffuser flowarea profile or a complex internal shock structure in the lip region,which reduce inlet pressure recovery and flow pumping efficiency, aswell as undermine diffuser flow stability.

However, as understood in the art, as supersonic design speed increases,so does the amount of compression necessary to decelerate the flow to afixed terminal shock Mach number. Additional compression implies theneed for more flow-turning off of the inlet axis, resulting in acorresponding increase in the cowl lip angle (in order to align the cowllip angle with the local flow at the terminal shock). Any increase incowl lip angle results in additional inlet frontal area, increasinginlet drag as speed increases. This adverse trend is a key reason whyconventional external compression inlets lose viability at highsupersonic Mach numbers.

One attempt to control cowl lip drag, as discussed in U.S. Pat. No.6,793,175 issued to Sanders, includes configuring the inlet to minimizethe shape and size of the cowl. Sanders'concept involves morphing atraditional rectangular intake into a more complex, but higherperformance, 3-D geometry that, in a frontal view, initially resembles acircumferential sector of an axisymmetric intake, but now with thecompression surface on the outer radius and the cowling on the innerradius. The cowl side extends across a similar circumferential angulararc in a frontal view, but because is it located on an inner radius, thephysical arc of the cowl is reduced. The cowl drag is said to beeffectively lessened through a reduction in transcribed circumferentialdistance. The practicality of this inlet concept is reduced by aircraftintegration challenges created by the 3-D geometry. For example, thecross-sectional shape may be more difficult to integrate from apackaging perspective than an equivalent axisymmetric design for poddedpropulsion systems. In addition, the complex inlet shape is likely tocreate complex distortion patterns that require either large scalemitigating techniques in the subsonic diffuser or the use of engineswith more robust operability characteristics.

Another method to reduce cowl lip angle to reduce drag involvesdecreasing the flow turn angle by increasing the inlet terminal shockMach number. However, the improvement in installed drag in using ahigher terminal shock Mach number is often offset by the loss in thrustfrom the reduction in pressure recovery resulting from the strongerterminal shock. As understood by those in the art, increasing theterminal shock Mach number also encounters significant limitations inpractice once viscous flow effects are introduced. Higher terminal shockMach numbers aggravate the shock-boundary layer interaction and reduceshock base boundary layer health. The increase in shock strength in thebase region also reduces inlet buzz margin, reducing subcritical flowthrottling capability. Additionally, the increase in terminal shock Machnumber ultimately increases the likelihood for the need of a complexboundary layer management or inlet control system

Inlet compression surfaces are typically grouped as either ‘straight’ or‘isentropic.’ An isentropic surface generally represents a continuouslycurved surface that produces a continuum of infinitesimally weakshocklets during the compression process. By contrast, a straightsurface generally represents flat ramp or conic sections that producediscrete oblique or conic shocks. While an inlet employing an isentropicsurface can have theoretically better pressure recovery than an inletemploying a straight-surface designed to the same operating conditions,real viscous effects combine to reduce the overall performance ofisentropic inlets and can lead to poorer boundary layer health whencompared to their equivalent straight-surface counterparts. Bothstraight and isentropic inlet types conventionally designed to the sameterminal shock Mach number also produce similar flow turn angle at thecowl lip and, consequently, similar cowl lip angles. As such, neitherthe straight-surface inlet design nor the conventional isentropic inletdesign provides a cowl drag benefit relative to the other.

As such, conventional design provides no significant latitude foradjusting the geometric arrangement of inlet and the cowl lip whendesigning a mechanically simple inlet compression surface usingconventional shock-on-lip focusing. Because the isolated cowl dragcharacteristics are relatively inflexible, inlet drag relief hashistorically been limited to minimizing inlet-airframe interferenceeffects.

SUMMARY OF THE INVENTION

Embodiments of the invention employ a relaxed isentropic compressionshaping of the compression surface of an inlet design. As used herein,the term “relaxed isentropic compression” surface refers to anisentropic compression surface characterized by a series of Mach linesin which at least a plurality of those Mach lines do not focus on thefocus point where the initial shock and the terminal shock meet. Thislack of Mach line focusing results in a total level of compression lessthan the level of compression generated by a conventional isentropiccompression surface designed to the same criteria. The relaxedisentropic compression design approach may be applied to any externalcompression or mixed compression inlet concept, including axisymmetric,partial conic, and two-dimensional intakes. The cowling angles forexternal compression inlets designed with a relaxed isentropiccompression surface may be reduced to approach those employed bytraditional mixed compression inlets, merging the inherent shockstability robustness of external compression geometry with the highinstalled performance of mixed compression geometry.

To be explained more fully below, relaxed isentropic compression inletshaping provides an increase in the design latitude for lofting theinlet cowling region while permitting control over other key inletdesign parameters such as terminal shock Mach number, diffuser flowdistortion, and total pressure recovery. The relaxed isentropiccompression inlet shaping may also enable a reduction in cowling surfaceangles and, as a result, may be configured to improve inlet drag andinterference drag characteristics. The reduced slope of the cowling mayalso lower the contribution of the inlet to the overall vehicle sonicboom characteristic during supersonic flight and decrease the potentialfor aerodynamic cross-interference between close-coupled inlets.

Embodiments of the invention may includes a supersonic inlet comprisinga leading edge configured to generate an initial shock wave and acompression surface positioned downstream of the leading edge and havingat least one curved section configured to generate isentropiccompression. The supersonic inlet may also include a cowl lip spatiallyseparated from the compression surface such that the cowl lip and thecompression surface define an inlet opening for receiving a supersonicflow. The compression surface may be configured to generate a secondshock wave that, during operation of the supersonic inlet at apredetermined cruise speed, extends from the compression surface tointersect the initial shock wave at a point substantially adjacent tothe cowl lip. The isentropic compression generated by the curved sectionmay be characterized by a series of Mach lines where, during operationof the supersonic inlet at the predetermined cruise speed, at least aplurality of the Mach lines do not focus on the point substantiallyadjacent to the cowl lip.

BRIEF DESCRIPTION OF THE DRAWINGS

While the specification concludes with claims particularly pointing outand distinctly claiming embodiments of the invention, it is believed thesame will be better understood from the following description taken inconjunction with the accompanying drawings, which illustrate, in anon-limiting fashion, the best mode presently contemplated for carryingout embodiments of the invention, and in which like reference numeralsdesignate like parts throughout the Figures, wherein:

FIG. 1-A shows a cross-section of a conventional straight-surfaceexternal compression inlet;

FIG. 1-B shows an inviscid flow solution for the conventionalstraight-surface external compression inlet shown in FIG. 1-A;

FIG. 2-A shows a cross-section of a relaxed isentropic compressionexternal compression inlet in accordance with an embodiment of theinvention;

FIG. 2-B shows an inviscid flow solution for the traditional isentropiccompression surface;

FIG. 2-C shows an inviscid flow solution for the relaxed isentropiccompression surface shown in FIG. 2-A;

FIG. 3-A shows a cross section of a relaxed isentropic compressionexternal compression inlet and subsonic diffuser in accordance with anembodiment of the invention demonstrating an example of poorcross-sectional area matching between intake and engine;

FIG. 3-B shows a cross section of a relaxed isentropic compressionexternal compression inlet and subsonic diffuser in accordance with anembodiment of the invention demonstrating an example of goodcross-sectional area matching between intake and engine;

FIG. 4-A shows a centerline cross section of a conventional biconic ortwin straight surface axisymmetric external compression inlet designedfor Mach 1.9 local flow speed;

FIG. 4-B shows a centerline cross section of a relaxed isentropiccompression axisymmetric external compression inlet designed for Mach1.9 local flow speed in accordance with an embodiment of the invention;

FIG. 5-A shows inviscid total pressure recovery results at Mach 1.9 forvarious conventional axisymmetric uniconic and biconic inletconfigurations;

FIG. 5-B shows inviscid total pressure recovery results at Mach 1.9 forvarious axisymmetric isentropic inlet configurations in accordance withan embodiment of the invention;

FIG. 6-A shows cowl drag coefficient results at Mach 1.9 for variousconventional axisymmetric uniconic and biconic inlet configurations;

FIG. 6-B shows cowl drag coefficient results at Mach 1.9 for variousaxisymmetric isentropic inlet configurations in accordance with anembodiment of the invention;

FIG. 7-A shows specific fuel consumption results at Mach 1.9 for variousconventional axisymmetric uniconic and biconic inlet configurations;

FIG. 7-B shows specific fuel consumption results at Mach 1.9 for variousaxisymmetric isentropic inlet configurations in accordance with anembodiment of the invention;

FIG. 8-A shows a half-plane CFD-based Mach number solution at Mach 1.9for a conventional axisymmetric biconic inlet configuration;

FIG. 8-B shows a half-plane CFD-based Mach number solution at Mach 1.9for an axisymmetric isentropic inlet configuration in accordance with anembodiment of the invention;

FIG. 9-A shows half-plane CFD-based Mach number solutions for variousmass flow ratios or MFR at Mach 1.9 for a conventional axisymmetricbiconic inlet configuration;

FIG. 9-B shows half-plane CFD-based Mach number solutions for variousmass flow ratios or MFR at Mach 1.9 for a axisymmetric isentropic inletconfiguration in accordance with an embodiment of the invention;

FIG. 10 shows CFD-based mass flow ratio data as a function of inlet massflow plug area at Mach 1.9 for various axisymmetric conventional inletsand isentropic inlets according to an embodiment of the invention;

FIG. 11 shows CFD-based total pressure recovery data as a function ofmass flow ratio at Mach 1.9 for various axisymmetric conventional inletsand isentropic inlets according to an embodiment of the invention;

FIG. 12 shows CFD-based additive drag coefficient data as a function ofmass flow ratio at Mach 1.9 for various axisymmetric conventional inletsand isentropic inlets according to an embodiment of the invention;

FIG. 13 shows CFD-based cowl drag coefficient data as a function of massflow ratio at Mach 1.9 for various axisymmetric conventional inlets andisentropic inlets according to an embodiment of the invention;

FIG. 14-A shows CFD-based specific fuel consumption data as a functionof mass flow ratio at Mach 1.9 for various axisymmetric conventionalinlets and isentropic inlets according to an embodiment of theinvention;

FIG. 14-B shows CFD-based specific fuel consumption data atnear-critical flow at Mach 1.9 for various axisymmetric conventionalinlets and isentropic inlets according to an embodiment of theinvention;

FIG. 15 shows CFD-based cowl drag coefficient as a function of mass flowratio at on- and off-design local Mach numbers for an axisymmetricconventional inlet and an isentropic inlet according to an embodiment ofthe invention;

FIG. 16-A through FIG. 16-C show a top view, front view, and side view,respectively, of a supersonic jet aircraft configuration;

FIG. 17 shows a CFD-based pressure solution of wing and fuselagesurfaces at freestream Mach 1.8 for a conventional axisymmetric inletinstalled on the left side of the aircraft and an axisymmetricisentropic inlet according to an embodiment of the invention installedon the right side of the aircraft; and

FIG. 18 shows the study aircraft sonic boom signatures at Mach 1.8cruise speed for a conventional axisymmetric inlet on the study aircraftand an axisymmetric isentropic inlet according to an embodiment of theinvention on the study aircraft.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure will now be described more fully with referenceto the Figures in which various embodiments of the invention are shown.The subject matter of this disclosure may, however, be embodied in manydifferent forms and should not be construed as being limited to theembodiments set forth herein.

Embodiments of the invention relate to supersonic inlet shaping whichimproves the net propulsive force through relaxed isentropic compressionsurfaces. As discussed above, “relaxed isentropic compression” refers toan isentropic compression surface characterized by a series of Machlines that do not necessarily focus at the point where the initialoblique shock and the terminal shock meet. In accordance withembodiments of the invention, overall performance improvement may beaccomplished using relaxed isentropic compression inlet configurationseven when the inlet exhibits relatively poor total pressure recoverycharacteristics. Further, inlets employing relaxed isentropiccompression shaping may achieve net improvements without reliance oncomplicated secondary systems or variable geometry.

FIG. 1-A shows a cross-section of a straight-surface externalcompression inlet 100 configured using shock-on-lip focusing. The inlet100 includes a compression surface 110 having a twin straight surfaceconstruction with a first straight surface 111 at an initial turn angle110 a and a second straight surface 112 at a second turn angle 110 b.The inlet 100 also includes a cowl lip 120 which is positioned at a cowlangle of 110 c measured off the centerline of the inlet 100. Thecompression surface 110 transitions to the shoulder 130 which definesthe throat 135, the narrowest portion of the inlet 100 flowpath. Afterthe throat 135, a diffuser 140 provides a divergent flow path deliveringsubsonic flow to the engine (not shown in FIG. 1-A).

During flight, the inlet 100 encounters supersonic flow in the directionindicated by the arrow A and captures air flow shown in the region B. Aninitial shock 200 forms when the supersonic flow initially encountersthe apex of compression surface 110. A secondary shock 210 forms at thetransition between the first straight surface 111 and the secondstraight surface 112 of the compression surface 110. Finally, a terminalshock 220 forms at the transition between the second straight surface112 and the shoulder 130. A cowl shock 230 is shown extending upward offthe cowl lip 120. As shown in FIG. 1-A, it should be noted that theinitial shock 200, the secondary shock 210 and the terminal shock 220are focused at the shock focus point 240. Shock focusing at or in closeproximity to the cowl lip is used to maximize the capture flow area B toreduce additive drag caused by excess flow spillage around the inlet.

FIG. 1-B shows an inviscid flow solution for the straight-surfaceexternal compression inlet 100 shown in FIG. 1-A. An inviscid flowsolution, where the solution does not account for viscosity of thefluid, may be acquired using analytical techniques such asmethod-of-characteristics (MOC). The basic computational techniques thatdefine the underlying method-of-characteristics process are well-knownto those skilled in the art and are available as code in the publicdomain. Compared to viscous results from higher order tools, such ascomputational fluid dynamics (CFD), inviscid solutions can be obtainedrapidly and without the need for extensive computation resources.Inviscid solutions usually possess a level of fidelity adequate forperforming initial parametric surveys and definition of the designspace. However, as would be apparent to those of skill in the art, CFDanalysis, and even hand calculations, could be used exclusively as ananalytical tool.

The inviscid flow solution shown in FIG. 1-B of the straight-surfaceinlet shown in FIG. 1-A illustrates the standard design concept of shockfocusing at the cowl lip region 240. The solution characteristic meshillustrates the initial shock 200, the secondary shock 210 and theterminal shock 220 and visually demonstrates the compression of thesupersonic flow prior to the terminal shock 220. As understood by thoseof skill in the art, the shock focusing may be designed with some marginbuilt in by focusing the shocks some short distance before the cowl lipto accommodate shock position fluctuations resulting from variations invehicle speed and atmospheric and air flow anomalies.

FIG. 2-A shows a cross-section of a relaxed compression or modifiedisentropic external compression inlet 300 in accordance with anembodiment of the invention. The inlet 300 includes a compressionsurface 310 having an initial straight surface 340 configured at aninitial turn angle 310 a. The compression surface 310 also includes asecond compression surface 311 that includes a curved section 312followed by a straight section 313. Although only the curved section 312of the second compression surface 311 generates isentropic compression,the entire compression surface 310 may be referred to herein as arelaxed isentropic compression surface. For comparison, an example of atraditional isentropic compression surface 500 is shown in a dashedline. The inlet 300 includes a cowl lip 320 which is positioned at acowl angle of 310 b measured off the centerline of the inlet 300. Thecompression surface 310 transitions into the shoulder 330 which definesthe throat 335, the narrowest portion of the inlet 300 flow path. Afterthe throat 335, a subsonic diffuser 350 provides a divergent flow pathdelivering subsonic flow to the engine (not shown in FIG. 2-A).

As with the inlet shown in FIG. 1-A, the inlet 300 encountersfree-stream supersonic flow in the direction indicated by the arrow Aand captures air flow shown in the region B. While an initial shock 400forms when the supersonic flow initially encounters the compressionsurface 310, it should be noted that the compression surface 310 doesnot generate the secondary shock shown in FIG. 1-A. A terminal shock 410forms at the transition between the compression surface 310 and theshoulder 330. A cowl shock 420 is shown extending upward off the cowllip 320. As shown in FIG. 2-A, the initial shock 400 and the terminalshock 410 are focused at the shock focus point 430.

Using conventional design practice and analytical tools such as MOC andCFD, a traditional isentropic compression surface 500, shown in a dashedline on FIG. 2-A (the terminal shock associated with the traditionalisentropic compression surface 500 is not shown in FIG. 2-A), may begenerated for a given inlet type and design conditions. FIG. 2-B showsan inviscid flow solution for the traditional isentropic compressionsurface 500 in FIG. 2-A. In accordance with traditional isentropicdesign practice, the initial shock 510 and the terminal shock 520 arefocused at the region of the cowl lip 320, forming a focus point 530.Additionally, the traditional isentropic compression surface 500includes an initial straight surface 540 followed by a curved section550, which may be configured to generate isentropic compression of thesupersonic flow. The curved section 550 may be followed by anotherstraight section 560. As understood by those of skill in the art and asillustrated by the inviscid flow solution in FIG. 2-B, a traditionalisentropic compression surface 500 is characterized by focusing the Machlines radiating from the curved section 550 at the focus point 530. Asshown in FIG. 2-B, Mach lines generated by the curved section 550illustrate isentropic compression as the Mach lines coalesce along theirlength, eventually focusing at the focus point 530.

Using the traditional isentropic compression surface as a baseline,analytical tools, such as MOC and CFD, may be used to define a relaxedisentropic compression geometry with an average level of compressionless than the traditional isentropic compression surface. Boundaryconditions, such as level of compression, local Mach number (forexample, overwing Mach number), terminal shock Mach number, initialconic or turning angle, and others known in the art, may be used by theanalytical tools to identify the surface geometry that achieves theboundary conditions. Iterative changes to the boundary conditions may beused to modify the geometry of the compression surface 310 in acontrolled and predictable manner, providing an approach for arriving ata desirable design target (for example optimizing the compressionsurface of a relaxed isentropic inlet for a particular engine).

As used herein, compression references the difference in Mach numberbetween a location immediately aft of the initial shock 400 and the Machnumber averaged along the terminal shock 410. The level of compressionof a relaxed isentropic compression surface references the differencebetween the compression of a traditional isentropic compression surfaceand the compression of a relaxed isentropic compression surface, whenboth surfaces are designed to the same design conditions. As would beunderstood by those of skill in the art, analytical tools may beconfigured to use various input values (for example, the averageterminal shock Mach number, level of isentropic compression, etc.) tobias the compression surface 310. As an example, the compression surface310 may be biased in order to control the target Mach number at the base410 a of the terminal shock 410.

Other methods or approaches may also be applied to generate isentropiccompression geometry 310. For instance, the surface shaping could beproduced based on alternate design metrics other than the level ofcompression. Alternate metrics may include, but should not be limitedto, flow angle distribution along the length of the terminal shock oraverage flow distortion.

FIG. 2-C shows an inviscid flow solution for the embodiment of therelaxed isentropic compression inlet design shown in FIG. 2-A. As shown,the initial shock 400 and the terminal shock 410 converge at the regionof the cowl lip 320. Contrary to the Mach lines shown in FIGS. 1-B and2-B, the plotted Mach mesh solution of FIG. 2-C illustrates how theseries of Mach lines radiating from the curved section 312 do not focusat the focus point 430. Instead, the Mach lines in FIG. 2-C include arelaxed region of compression, shown in region 450 of FIG. 2-C, that isdirected into the inlet opening or away from the cowl lip 320. Ratherthan focusing entirely on the focus point 430, as shown in FIG. 2-B, theMach lines in region 450 spread toward the compression surface 310 andintersect the region 450 of the terminal shock. As would be apparent toone of ordinary skill in the art, the diffused nature, or lack of focuson the focus point 430, of the Mach lines indicates that some of thetraditional flow compression in the vicinity of the cowl lip, as shownin FIG. 2-B is now spreading inward, towards the compression surface310, instead of being constrained to the vicinity of the focus point 430in front of the cowl lip 320.

As a result, the upper (or outer annular region of an axisymmetricinlet) region of the captured flow area, in the region 450, experiencesdefocused or relaxed compression, and, as a consequence, experiencesless local flow turning at the cowl lip. The less local flow turning inthe region of the cowl lip 320 results in a lower cowl lip angle 310 b,as shown in FIG. 2-A, when the cowl lip is aligned with the local flowat the cowl. As described in greater detail below, a lower cowl lipangle, in accordance with embodiments of the invention, may be used toreduce cowl drag.

As shown in FIGS. 2-A and 2-C, the terminal shock 410, at its base 410a, is substantially orthogonal to the compression surface but,thereafter, exhibits bending or curvature as the terminal shockapproaches the cowl lip region. The observed bowing or curvature isdriven by a velocity gradient along the length of the terminal shock.The velocity gradient of the terminal shock spans a larger Mach rangefrom compression surface to cowl lip than the velocity gradient of theterminal shock 410 shown in FIGS. 1-A and 1-B or the terminal shockshown in FIG. 2-B. The level of terminal shock bowing, in FIG. 2-A, inthe vicinity of the cowl lip 320 is representative of the local flowangle in the vicinity of the cowl lip. As the bowing becomes morepronounced due to decreased local compression 440 resulting from relaxedisentropic compression geometry 310, the local flow angle aligns itselfmore closely to the freestream flow direction. This is seen in thecurvature of the region 450 as the terminal shock approaches the focuspoint 430. Because the cowling is also aligned to the local flow angleat the cowl lip 320, the cowl angle 310 b is reduced.

In accordance with embodiments of the invention, the compression surface310 uses a relaxed isentropic compression surface with a compressionprocess distributed more prominently towards the base 410 a of theterminal shock 410. While the compression surface 310 generates lesscompression than the traditional isentropic compression surface 500, thecompression surface 310 may be configured to retain, at the base of theterminal shock, a target terminal shock Mach number similar to that of atraditional isentropic compression solution for an inlet designed to thesame key inlet design parameters. By retaining a similar terminal shockMach number at the base 410 a, the relaxed isentropic compression inletmay be configured to avoid introducing a severe shock-boundary layerinteraction.

The terminal shock Mach number at the base of the terminal shock may bemaintained using an relaxed isentropic compression surface, although aloss of total pressure recovery may be observed due to the flowcompression spreading inward and aft of the terminal shock in the region450 near the cowl lip 320. As understood in the art, a loss of totalpressure recovery may result in a reduction in engine performance. Asshown in detail below, the reduction in cowl drag, as a result of areduced cowl lip angle, offsets the reduction in engine performanceresulting from the observed loss in total pressure recovery. Further,the mechanical simplicity of the inlet design shown in FIG. 1-A may beretained in relaxed isentropic compression inlet designs in accordancewith embodiments of the invention.

It should be noted that the compression surface 310 shown in FIG. 2-Amay be considered a hybrid design. The relaxed isentropic compressioninlet design, in accordance with embodiments of the invention, includesan initial straight-surface 340 at the leading edge of the compressiongeometry and an isentropic shaping on the second compression surface311.

FIG. 3-A shows a cross section of an axisymmetric relaxed isentropiccompression external compression inlet 600 and subsonic diffuser 620 inaccordance with an embodiment of the invention demonstrating an exampleof poor area matching between intake and engine. Understanding of thematching characteristics between intake capture area and maximum nacellearea may help determine the magnitude of the installed drag benefit thatcan be realized using relaxed isentropic compression. For example, anintake area 601, as shown in FIG. 3-A, that is small compared to themaximum nacelle area 602 results in a geometric cowl profile that maynot benefit as significantly from a reduction in cowling angle at theinlet lip 610. Poor area matching results in a large cowl frontal area,defined as the difference in maximum nacelle area 602 and intake area601. As frontal area grows, the nacelle loft lines 630 become moredifficult to significantly influence through shaping at the cowl lip610, reducing the drag and sonic boom improvement available throughrelaxed isentropic compression geometry.

Higher specific flow capability is a hallmark of modern turbo machinerydesign, and the greater flow demand for a given fan size permits theinlet capture diameter to grow relative to the engine diameter. This maybe used in combination with embodiments of the invention to enable amore streamlined match between intake area at the inlet and the maximumnacelle area as shown in FIG. 3-B.

FIG. 3-B shows a cross section of an axisymmetric relaxed isentropiccompression external compression inlet 700 and subsonic diffuser 720 inaccordance with an embodiment of the invention demonstrating an exampleof good matching between intake and engine. As shown in FIG. 3-B, forexample, an intake area 701 approaches the maximum nacelle area 702resulting in a geometric cowl profile that may significantly benefitfrom a reduction in cowling angle at the inlet lip 710. For inletgeometry 700 that is well matched between intake diameter 701 andmaximum nacelle diameter 702, reductions in cowling angle can produce amore streamlined lofting that extends further aft along the nacelle andwhich can produce more significant improvements in drag and sonic boomcharacteristics compared to those resulting from an inlet having poorarea matching. As such, intake-to-engine area matching may be tailoredto fully capture the drag and sonic boom benefits of the relaxedisentropic compression inlet design.

As discussed above, the performance benefits enabled by reduction incowl lip angle may be offset elsewhere in the inlet design. Relative toa conventional inlet, for example inlet 100 of FIG. 1-A, an relaxedisentropic compression inlet, designed to the same operating conditions,may experience increased flow distortion and additional boundary layerthickness within the subsonic diffuser. For some relaxed isentropiccompression inlet configurations, a reduction in total pressure recoveryis also witnessed due to higher supersonic Mach number along the outerlength of the terminal shock.

Further, the strong velocity gradient produced by relaxed isentropiccompression along the length of the terminal shock, particularly as thecowl lip is approached, creates a less uniform post-shock velocity andpressure field within the diffuser. The less uniform post-shock velocityand pressure field may be seen by the engine as an increase indistortion. As understood by those in the art, the additional distortionmay be tolerated by the turbo machinery provided that much of the flowdefect passes through the fan, avoiding entrainment by the moresensitive compressor. As would be apparent, this may be achieved usinghigher bypass engines or engines that divert a higher ratio of flowaround, as opposed to through, the compressor. However, it should beunderstood that other engine configurations are contemplated and may beused with inlets in accordance with the invention.

Additionally, it should be understood that the boundary layer behind thebase of the terminal shock may increase as a result of the inner surfacegeometry changes required to smoothly decelerate the captured flow intothe engine face. As the cowl lip angle is reduced, the diffuser surfaceangle may also be reduced immediately behind the base of the terminalshock to maintain the diffusion area profile. As a result, a morepronounced turn-angle may be introduced immediately aft of the base ofthe terminal shock on the diffuser shoulder instead of a more smoothlytransitioning surface into the subsonic diffuser. This angle-break orlarge turn-angle amplifies post-shock flow reacceleration near theshoulder's peak and increases the downstream boundary layer thickness.

In determining the effectiveness of various embodiments of theinvention, a cost function based on specific fuel consumption (SFC) waschosen for comparing the relative benefits of the relaxed isentropiccompression inlet concept against those of conventional straight-surfaceconfigurations. The initial analysis relied on inviscid flow analysis topopulate the cost function for embodiments of the relaxed isentropiccompression inlet. Additionally, some embodiments and/or key results ofthe relaxed isentropic compression inlet design were assessed usingOverflow, a higher fidelity, three-dimensional, viscous computationalfluid dynamics (CFD) software package developed by NASA.

The inviscid inlet compression analysis was conducted usingmethod-of-characteristics based analytical tools. A MOC program may beconfigured to operate in a design mode option in which thecharacteristics of a compression surface, for example, local freestreamMach number, terminal shock Mach number, surface angles, andshock-off-lip margin, are input. The MOC program may then be configuredto generate the compression surface geometry and cowl lip coordinatesrequired to meet the prescribed boundary conditions. Once a surface hasbeen defined, the geometry definition may then be employed within theMOC code in a direct analysis mode, in which the prescribed geometry maybe evaluated at off-design conditions or in combination with a nacelleouter wall geometry definition.

It should be understood that the MOC code is capable of running bothtwo-dimensional and axisymmetric inlet arrangements using singlestraight-surface, multi-straight-surface, or relaxed or traditionalisentropic compression surfaces. User-defined surface Mach numberdistributions may also be input as boundary conditions to define acustom surface. Note that terminal shock Mach number cannot be specifiedfor straight inlet compression surface arrangements, as it is a fall-outof a given configuration. However, for isentropic surfaces, terminalMach number is a required input in order to provide MOC with anobjective target for the completion of the isentropic flow turningprocess along the compression surface.

In addition to geometric surface definition and cowl lip location, keyoutput parameters from the MOC code include shock train total pressurerecovery, additive (spillage-related) drag coefficient, cowl shock wavedrag coefficient, and flow distortion. Also computed is a spatialdefinition of the terminal shock geometry, including local pre-shock andpost-shock Mach number and flow angle along the length of the shock.Local Mach number and coefficient of pressure data are also computedalong the compression surface from freestream to the base of theterminal shock. As with FIGS. 1-B, 2-B and 2-C, the MOC solution meshcan be graphically plotted in order to visualize the arrangement ofshock waves and Mach lines.

The CFD analysis was performed using NASA's Overflow, afinite-difference, Reynolds-averaged computer code available to thepublic and used to model the flowfield within and about theinlet-nacelle-diffuser configuration. The code uses a time-dependentintegration from an initial condition, usually freestream, which thenconverges to a steady-state solution. The computer code employsstructured overset griding as well as inviscid and viscous modelingoptions. Post-processing calculations were used to identify keyparameters such as subsonic diffuser pressure recovery, additive drag,cowl drag, flow distortion descriptors, tip and hub flow blockage, andinstalled SFC.

The SFC-based cost equation used for the analysis process follows thetypical format for an installed powerplant arrangement with additivedrag and cowl drag subtracted from net thrust within the equation. Theformula references a baseline (straight-surface) inlet configuration.The equation follows:

${\Delta\;{SFC}_{Installed}} = {\frac{{WFE}_{Base} + {\left( {ɛ - ɛ_{Base}} \right)\frac{\delta\;{WFE}}{\delta ɛ}}}{{FN}_{Base} - D_{Add} - D_{Cowl}} - {SFC}_{{Installed}_{Base}}}$

The equation variables are defined as:

ε inlet total pressure recovery

DAdd additive drag, lbf

DCowl cowl drag, lbf

FN net thrust, lbf

SFC specific fuel consumption, lbm/hr/lbf

WFE engine fuel flow, lbm/hr

It should be understood that the departure in total pressure recoveryrelative to baseline is accommodated through an engine cycle-basedderivative that describes the change in fuel flow at constant thrust andconstant physical engine airflow. This derivative was linearized atsupersonic design cruise speed using a three-point recovery survey forthe applied study engine. The outer surface of the nozzle was modeled asa straight conic surface, but its associated drag was not included inthe cowl drag term.

All analysis was performed assuming steady-state conditions usingfixed-geometry, axisymmetric, fully external compression and a designspeed of Mach 1.9, corresponding to the assumed local Mach number at afreestream aircraft cruise speed of Mach 1.8. A constant terminal shockMach number of 1.3, measured at base of shock, was chosen to balanceperformance and flow stability issues. As known in the art, the initialconic shock originating from the compression surface spike tip wasplaced close to the cowl lip at design speed for low flow spillage.

In analyzing the straight compression surface using the initialMOC-based analysis, a wide variety of configurations were considered.Uniconic (single straight) surface designs having initial conichalf-angles from 8 deg to 34 deg, measured relative to centerline, wereevaluated in increments of 2 deg. Biconic (two straight) surface designswere also evaluated and included all surface combinations of initialconic half-angles from 8 deg to 34 deg (in 2 deg. increments) and secondsurface turn-angle from 2 deg to 16 deg (in 2 deg. increments). Shockdetachment limited the maximum level of total turning angle that couldbe analyzed.

A naming convention is used to describe each configuration's compressionsurface geometry. For the straight-surface family, a four digitnomenclature was employed, the first two digits referring to the inlet'sinitial conic half-angle, the second two digits representing theadditional turn-angle provided by the second surface. For example, 1016Biconic is a straight-surface inlet configuration with 10 deg of initialhalf-angle for the initial compression surface followed by 16 deg ofadditional turning on the second conic surface.

FIG. 4-A shows a centerline cross section of a conventional biconicaxisymmetric external compression inlet 800 designed for Mach 1.9 localflow speed. The biconic straight-surface inlet 800 was used as abaseline reference inlet, for purposes of analysis, and employed an 18degrees of half-angle 801 a turning on the initial cone compressionsurface 801 and an additional 8 degrees of turning 802 a on the secondcompression surface 802. The baseline inlet 800 also includes acenterbody shoulder reverse angle 803 of 3.1 degrees. Shoulder reverseangle refers to the angle between the aft end of the compression surfacerelative to the surface immediately downstream at the point where theflow path transitions into the subsonic diffuser. The magnitude of theshoulder reverse angle is determined by several design variablesincluding the diffusion profile required by the applied engine cycle andthe magnitude of the cowl angle. For example, at constant terminal shockMach number, a smaller cowl angle requires a larger reverse angle tomaintain the same subsonic diffusion profile. If the reverse angle wasnot increased as cowl angle was decreased, a significant contraction ofthe downstream subsonic flow path could otherwise occur, incontradiction to the design requirements of an external compressioninlet.

The inlet 800 generates a local flow angle at the cowl lip 804 of 14.1degrees with an outer cowl lip angle 804 a of 19.5 degrees. The angle ofthe surface on the inside of the cowling at the lip is aligned with thelocal flow angle at the terminal shock. As explained earlier, thisdesign practice prevents the formation of complex shocks or adverse flowconditions at the cowl lip. Therefore, the local flow angle at the cowllip, defined earlier, determines the initial angle along the insidesurface of the cowling. By necessity, the outer cowl angle will belarger than the angle on the inside cowl surface in order to providewall volume for structural and manufacturing considerations and topermit a smooth transition of the lofting from the cowl lip aft to themaximum nacelle diameter. For this inlet example, an outer cowl angle of19.5 degrees was selected to meet these design requirements. Thisconfiguration, given the designation 1808 Biconic in accordance with thenaming convention, is known in the art to provide reasonable totalpressure recovery and terminal shock Mach number, as shown in theanalysis below.

For the relaxed isentropic compression surfaces in accordance withembodiments of the invention, initial conic half-angles from 7 deg to 26deg were studied at increments no greater than 2 deg. Isentropiccompression values ranging from 20 percent to 100 percent, in incrementsno larger than 10 percent, were evaluated at each initial conichalf-angle increment. Note that 100 percent compression represents atraditionally designed isentropic surface (non-hybrid) while 0 percentrepresents a straight surface, where none of the compression aft of theinitial straight surface is attributable to isentropic compression.

A naming convention is also used for the relaxed isentropic compressionfamily. A four digit naming convention identifies the characteristics ofthe relaxed isentropic compression inlet with the first two digits againreferring to initial conic half-angle. The second two digits, however,represent the level of isentropic compression in percent. For example,1280 Isentropic would be an relaxed isentropic compression inletconfiguration with 12 deg of initial conic half-angle for the initialcompression surface followed by an isentropic compression surfaceproducing 80 percent of full isentropic compression.

FIG. 4-B shows a centerline cross section of an isentropic axisymmetricexternal compression inlet 900 designed for Mach 1.9 local flow speed inaccordance with an embodiment of the invention. The relaxed isentropiccompression inlet 900 employed 8 degrees of half-angle turning 901 a onthe initial cone or compression surface 901. The relaxed isentropiccompression surface 902 generates a 90 percent level of compression. Therelaxed isentropic compression inlet 900 also includes a centerbodyshoulder reverse angle 903 of 11.5 degrees. The inlet 900 generates alocal flow angle at the cowl lip 904 of 3.2 degrees with an outer cowllip angle 904 a of 12.0 degrees. This inlet configuration, given thedesignation 0890 Isentropic in accordance with the naming convention, isa relaxed isentropic compression inlet in accordance with an embodimentof the invention that shows improvement in integrated airframeperformance and sonic boom assessment.

Both biconic and relaxed isentropic compression configurations employ asmall amount of bluntness at the cowl lip to avoid an impractical andimpossibly sharp leading edge geometry. In addition, the subsonicdiffuser flowpath was designed to slightly contract for a brieflongitudinal distance immediately aft of the base of the terminal shock.Slight initial contraction reduces the need for an immediate step-changein the shoulder turn angle that would otherwise be employed to rapidlyintroduce the required subsonic diffusion area profile. By reducing themagnitude of the turn angle, the tendency is minimized for the flow toreaccelerate at the base of the terminal shock at off-design,supercritical flow conditions, improving total pressure recovery anddownstream boundary layer health. It is known to those skilled in theart that initial flow path contraction on external compression inletscan be employed without detrimental impact to the overall performance ofthe inlet at on-design conditions provided that care is used in itsapplication.

An analytical turbofan engine cycle computer model was used for theanalysis presented herein. This cycle is representative of engines suchas the General Electric F404 turbofan and the Rolls-Royce Tay 650turbofan. The analytical engine consisted of a two spool high-bypassratio cycle with variable area nozzle. Operating temperaturecharacteristics were based on a hot section life requirement of 2000 hrat supersonic cruise. The engine configuration was sized for the thrustrequirements consistent with a 100,000 lb gross takeoff weight-classvehicle employing a twin-engine arrangement. The fan was sized to meetrequired takeoff thrust at a mean jet velocity capable of achievingStage IV airport noise requirements with 10 dB cumulative margin. Itshould be understood that embodiments of the invention may be employedon various engines and adjusted to optimize performance for a given setof engine flow characteristics.

The inlet and nacelle configurations used in the present study weresized based on the cruise airflow characteristics of this engine cycleoperating at maximum continuous power. The engine study cycle'srelatively constant corrected airflow schedule as a function of Machnumber eliminated the need for a variable inlet throat area controlsystem, permitting the employment of a fixed inlet centerbody geometryarrangement. Applying representative levels of aircraft bleed airextraction and horsepower offtake, the engine cycle model provided netthrust, fuel flow, and pressure recovery sensitivity information which,in conjunction with the SFC-based cost function, was used to evaluatethe inlet design.

FIGS. 5 through 7 show results from the MOC-based analysis in whichcontour plots are overlaid on the inlet design space to convey keyresults. The plots of the straight-surface inlet designs are shown inFIGS. 5-A, 6-A, and 7-A, which include the initial conic half-angleplotted on the horizontal axis and the second-surface turn angle plottedon the vertical axis. The plots of the isentropic inlet designs inaccordance with embodiments of the invention are shown in FIGS. 5-B,6-B, and 7-B, which include the level of compression in percent plottedon the vertical axis with the initial conic half-angle plotted on thehorizontal axis.

As would be apparent to those of skill in the art, terminal shock Machnumber varies as a function of the total flow turn-angle produced by theinlet compression surface. For an axisymmetric external compressioninlet designed to a local freestream value of Mach 1.9, a totalhalf-plane turn-angle of 26 deg provides a terminal shock Mach number ofapproximately 1.3, the value used as a design target for the analysisherein and representative of good design practice for ensuring adequateshock and flow stability. As such, it is only at 26 deg of totalturning, represented in FIGS. 5-A, 6-A, and 7-A as a dashed line throughthe conventional straight-surface design space, that objectivecomparisons can be made with the isentropic results, all of which alsowere generated using a target terminal shock Mach number of 1.3.

FIG. 5-A shows inviscid total pressure recovery results at Mach 1.9local flow speed for various conventional biconic inlet configurationsand FIG. 5-B shows inviscid total pressure recovery results at Mach 1.9local flow speed for various isentropic inlet configurations inaccordance with embodiments of the invention. Pressure recovery is seento generally increase as turning angle increases. An increase in turningangle produces an increase in overall upstream flow compression and,therefore, a reduction in the strength of the terminal shock. Thisdecrease in shock strength produces a corresponding decrease in pressureloss across the terminal shock. In FIG. 5-A, it should be noted thatrecovery performance is maximized along the line of constant 26 deg flowturning as it nears the 0.96 total pressure recovery contour and occursat about 18 degrees initial conic half-angle and 8 degrees secondsurface turn-angle or at the 1808 Biconic design point. In FIG. 5-B,pressure recovery also improves with level of compression. The 0890Isentropic design point, as indicated on the figure, shows similarrecovery pressure to 1808 Biconic. However, it should be noted that the0890 Isentropic purposely misses peak recovery potential for tradereasons that are indicated below.

FIG. 6-A shows cowl drag coefficient results at Mach 1.9 local flowspeed for various conventional biconic inlet configurations and FIG. 6-Bshows cowl drag coefficient results at Mach 1.9 local flow speed forvarious isentropic inlet configurations in accordance with embodimentsof the invention. Straight-surface drag values are nearly constant atequivalent total turn-angle because cowl angle varies little at aconstant terminal shock Mach number. As would be apparent to those ofskill in the art, the cowl angle and total drag increase as totalturn-angle increases.

As confirmed in FIG. 6-B, cowl drag decreases at fixed initialhalf-angle with decreasing compression level because decreasingcompression implies a simultaneous reduction in cowling angle.Limitations in intake-nacelle area matching for the engine cycleemployed force a local cowl drag minima region to form at lower initialconic half angles. In additional, larger initial conic half angles limitthe amount of compression required of the isentropic surface, reducingits effectiveness in lowering cowl angle and, therefore, drag.Nevertheless, it should be noted that the 0890 Isentropic exhibits amuch-improved cowl drag characteristic when compared to the 1808Biconic. As discussed above, this improvement may be attributed to thereduction in cowl angle as a result of less local flow turning at thecowl lip for the relaxed isentropic compression inlet designs. Foranalysis purposes, the inlet drag coefficient data are normalized usingthe cowl area for all isolated inlet results.

FIG. 7-A shows specific fuel consumption results at Mach 1.9 local flowspeed for various conventional biconic inlet configurations and FIG. 7-Bshows specific fuel consumption results at Mach 1.9 local flow speed forvarious isentropic inlet configurations in accordance with embodimentsof the invention. FIGS. 7-A and 7-B contrast installed SFC between thestraight-surface inlet design and embodiments of the relaxed isentropiccompression inlet design, with the results presented in terms of percentchange from the value computed for the baseline 1808 Biconic inlet.Therefore, a negative value represents improvement in SFC relative tothe reference point.

As indicated by the results in FIG. 7-A along the dashed linerepresenting constant total flow turn angle of 26 deg (constant terminalshock Mach number of 1.3), no improvement in SFC is seen relative to the1808 Biconic baseline point. This result is expected since nosignificant improvements in cowl drag or total pressure recovery arepossible along this line of constant turn angle as discussed previously.In fact, as shown in the figure, the 1808 Biconic baseline pointachieves the best SFC along the 26 deg line of constant turn-angle line.Larger turn angles (lower terminal shock Mach number) provide improvedpressure recovery, but this benefit is increasingly offset by additionalcowl drag resulting from the higher cowling angles. The net result ishigher SFC relative to the baseline point. Conversely, lesser turnangles result in limited improvement in SFC relative to the baselinepoint, but these results are irrelevant because the terminal shock Machnumber resulting from the lower turn angles is greater than thatdictated by common supersonic design practice.

As shown in FIG. 7-B, nearly all of the isentropic inlet design spaceshows improvement in SFC relative to the 1808 Biconic baseline point. Inthe isentropic design space, the cowl drag reduction (FIG. 6-B) producedby isentropic compression levels less than 100 percent trades favorablyagainst reduced total pressure recovery (FIG. 5-B) within the SFC-basedcost equation. As shown in FIG. 7-B, the estimated installed SFCimprovements of the relaxed isentropic compression inlet design 0890Isentropic is greater than 8 percent relative to the 1808 Biconic. Theseresults indicated that additional SFC improvement would be possible witha combination of even lower compression levels and higher initial conichalf-angles, but subsequent CFD analysis showed that viscous effectsprecluded significant improvement relative to the 0890 Isentropicconfiguration in this region of the design space, as discussed furtherbelow.

Relaxed isentropic compression inlet embodiments of the invention,including the 0890 Isentropic, were analyzed using higher fidelity CFDviscous analysis tools. The configurations were chosen to cover a fullrange of design parameters (initial half-angle and level ofcompression), operating characteristics (flow distortion and blockage),and installed performance. Two straight-surface inlet designconfigurations were selected along the 26 deg flow turning line for CFDviscous analysis: the baseline 1808 Biconic inlet and the 2600 Uniconicinlet. It should be noted that the 2600 Uniconic is similar to the inletdesign of the B-58 bomber, which was capable of Mach 2 flight speed.

FIG. 8-A shows a half-plane computational fluid dynamics (CFD) basedMach number solution at Mach 1.9 local flow speed for an 1808 Biconicinlet configuration with a fan face located at 850. FIG. 8-B shows ahalf-plane CFD based Mach number solution at Mach 1.9 local flow speedfor an 0890 Isentropic inlet configuration with a fan face located at860 in accordance with an embodiment of the invention. The CFD analysiswas performed at on-design cruise speed and near-critical airflow. InFIG. 8-A, the 1808 Biconic solution displays well-defined shockstructure and a strong cowl shock.

In FIG. 8-B, the 0890 Isentropic inlet shows evidence of compressionregion defocusing behind the initial conic shock. This compressiondefocusing is an artifact of the relaxed isentropic compression processand is discussed earlier. A weaker cowl shock resulting from a decreasedcowl angle is also evident, as shown in FIG. 4-B. The boundary layerthickness along the centerbody of the 1808 Biconic's diffuser in FIG.8-A appears to be less than the boundary layer thickness along thecenterbody of the 0890 Isentropic diffuser in FIG. 8-B, indicating theadverse influence of the additional turning angle at the centerbodyshoulder for the relaxed isentropic compression inlet.

FIG. 9-A shows a chart of half-plane CFD based Mach number solutions atvarious mass flow ratios (MFR, defined as the ratio of the mass flowcaptured by the inlet to the flow passing through the cowl lip areaprojected to freestream) at Mach 1.9 local flow speed for a 1808 Biconicinlet configuration and FIG. 9-B shows a chart of half-plane CFD basedMach number solutions at various mass flow ratios at Mach 1.9 for anisentropic inlet configuration in accordance with an embodiment of theinvention. As would be understood by those in the art, the mass flowratio was controlled in the CFD analysis by means of mass flow pluggeometry inserted in the downstream subsonic flow path.

Referring to FIG. 9-A, it should be noted that the terminal shock ispulled increasingly aft, into the diffuser, as mass flow ratio (plugarea) increases. At a mass flow ratio of 0.9786, a gap can be observedbetween the tip of the terminal shock and the cowl lip, indicating asmall amount of flow spillage (the flow is slightly subcritical). At amass flow ratio of 0.9876, the terminal shock is now essentiallyattached to the cowl lip, indicating minimal spillage (the flow isnear-critical). At a mass flow ratio of 0.9881, the flow is slightlysupercritical with the terminal shock entrained more deeply at its basewithin the diffuser. At a mass flow ratio of 0.9883, the super-criticalshock structure becomes more adverse, which, as would be apparent tothose of skill in the art, raises the boundary layer thickness andreduces downstream flow area to a value less than that at the intakeentrance. As a result of the increased boundary layer, the shock trainmay be expelled, with increased spillage. This expulsion of the shocktrain is evidenced by the final CFD solution in FIG. 9-A with an MFR of0.9119.

Referring to FIG. 9-B, the terminal shock is pulled increasingly aftwith increasing mass flow, as in FIG. 9-A. The solutions in FIG. 9-Bwere not carried to the point where the shock train was expelled, butthey provide substantiation that the relaxed isentropic compressioninlet can tolerate significant entrainment of the base of the terminalshock at super-critical flow values, like the Biconic inlet in FIG. 9-A.This is evidenced by the solutions in FIG. 9-B at MFR values of 0.9851and 0.9860 in which the terminal shock base is very deeply angled intothe subsonic diffuser flowpath. As indicated by the ability to supportsignificant entrainment of the terminal shock within the downstreamdiffuser at high MFR, both the 1808 Biconic in FIG. 9-A and the 0890Isentropic in FIG. 9-B show moderate tolerance for supercritical massflow.

FIG. 10 shows a graph plotting CFD based mass flow ratio (y-axis) as afunction of inlet mass flow plug area (x-axis) at Mach 1.9 local flowspeed for four inlet configurations: 1808 Biconic, 0890 Isentropic, 0895Isentropic, and 1470 Isentropic. Plotting MFR vs mass flow plug area canprovide an indication of the flow pumping capability of each inlet andany corresponding sensitivity to the influence of diffuser boundarylayer characteristics. For instance, inlets that exhibit a higher massflow for a given plug area suggests that those configurations experienceless downstream boundary layer-induced flow blockage. Also, an inletthat exhibits a downward break in mass flow ratio at a lower plug areaindicates that that configuration has a diffusion profile that is moresensitive to boundary layer buildup with increasing mass flow. From FIG.10, it can be seen that the inlets with higher compression levels passmore flow per unit plug area. This is because inlets with higher levelsof compression have lower centerbody shoulder reverse angles because ofthe higher cowling angles. A lower centerbody shoulder reverse angleproduces a more gentle downstream boundary layer and, therefore, lessflow blockage.

FIG. 11 shows a graph plotting CFD based total pressure recovery(y-axis) as a function of mass flow ratio (x-axis) at Mach 1.9 localflow speed for four inlet configurations: 1808 Biconic, 0890 Isentropic,0895 Isentropic, and 1470 Isentropic. Unlike the earlier results usingMOC, these CFD based analysis includes viscous subsonic diffuser losses.The near-critical flow region for each inlet configuration is evident inFIG. 11 based on the peak recovery point and the rapid loss of recoveryat higher flow values. Because of reduced terminal shock strength in thevicinity of the cowl lip, higher isentropic compression levels deliverbetter recovery. As noted before, the 0890 Isentropic inlet demonstratesslightly worse recovery characteristics than the 1808 Biconic.

FIG. 12 shows a graph plotting CFD based additive drag coefficient(y-axis) as a function of mass flow ratio (x-axis) at Mach 1.9 localflow speed for four inlet configurations: 1808 Biconic, 0890 Isentropic,0895 Isentropic, and 1470 Isentropic. Additive drag is that component ofinlet-generated drag resulting from excess flow spilling around theinlet. The data shown in FIG. 12 indicates that the difference in theadditive drag coefficient for the plotted inlet configurations is minorand the values small for the 1808 Biconic, 0890 Isentropic, 0895Isentropic inlets, provided that the inlets are flowing at near-criticalflow. As would be apparent to those of skill in the art, additive dragcoefficient increases very rapidly as flow spillage increases.

FIG. 13 shows a graph plotting CFD based cowl drag coefficient (y-axis)as a function of mass flow ratio (x-axis) at Mach 1.9 local flow speedfor four inlet configurations: 1808 Biconic, 0890 Isentropic, 0895Isentropic, and 1470 Isentropic. FIG. 13, like the MOC-based results inFIG. 6, demonstrates the potential performance differences between thestraight-surface inlet designs and the relaxed isentropic compressioninlet designs in accordance with embodiments of the invention. As shownin FIG. 13, the cowl drag steadily increases with MFR with the lowerlevels of isentropic compression producing the least amount of cowl dragdue to their lower cowl angles as discussed above. The conventional 1808Biconic inlet configuration displays a significantly greater amount ofcowl drag, in some cases over twice as much cowl drag, than the threeIsentropic inlets shown in FIG. 13.

It should be noted that, despite the lowest cowl drag data of anyconfiguration in FIG. 13, the 1470 Isentropic inlet was unable toachieve both low cowl drag and low spillage flow conditions. As shown inFIG. 12, the lowest attainable additive drag coefficient for the 1470Isentropic inlet is about 0.02 due to severe subsonic diffuser boundarylayer growth characteristics. As such, viscous effects prevented the1470 Isentropic inlet from achieving a low additive drag value whencompared to other relaxed isentropic compression inlet embodiments ofthe invention. This subsonic diffuser boundary layer growthcharacteristic is generally seen with all low compression relaxedisentropic compression inlets, precluding them from fully capitalizingon their otherwise low cowl drag features.

FIG. 14-A shows a graph plotting CFD based installed specific fuelconsumption (y-axis) as a function of mass flow ratio (x-axis) at Mach1.9 local flow speed for four inlet configurations: 1808 Biconic, 0890Isentropic, 0895 Isentropic, and 1470 Isentropic. The results shown inFIG. 14-A are generated using CFD based analysis and the SFC costequation presented above. As was done for the MOC-based results, the SFCdata is presented as a percentage of the baseline 1808 Biconic's valueat near-critical mass flow with negative values indicating relativeperformance improvement. The 0890 Isentropic inlet, at near-criticalflow, indicates about a 9.9 percent improvement over the baseline 1808Biconic at near-critical flow.

FIG. 14-B shows a graph plotting CFD based installed specific fuelconsumption (y-axis) in percent at near-critical flow at Mach 1.9 localflow speed for two conventional inlets and eight isentropic inlets inaccordance with embodiments of the invention. Although only the 1808Biconic, 0890 Isentropic, 0895 Isentropic, and 1470 Isentropic inletswere shown in FIGS. 10 through 14-A for clarity and simplicity, CFDanalysis was used to evaluate eight relaxed isentropic compressioninlets: 0890 Isentropic, 0895 Isentropic, 1070 Isentropic, 1090Isentropic, 1470 Isentropic, 1490 Isentropic, 1850 Isentropic, 1870Isentropic. The isentropic inlets were chosen to cover a full range ofdesign parameters (initial half-angle and level of compression),operating characteristics (flow distortion and blockage), and installedperformance. Again, the SFC data is presented as a percentage of thebaseline 1808 Biconic's value at near-critical mass flow with negativevalues indicating relative performance improvement.

Using results from the CFD analysis of the straight-surface inlets andthe relaxed isentropic compression inlets, the SFC data for each inletat near-critical flow is presented in FIG. 14-B. For those inletscapable of achieving near-critical mass flow and low additive drag (allbut 1070 Isentropic, 1470 Isentropic, and 1850 Isentropic), theCFD-based results mirror the MOC-based predictions, shown in FIG. 7-B.In FIG. 7-B and FIG. 14-B, performance improvements approaching 10percent are indicated for relaxed isentropic compression inletsemploying moderately high levels of compression (greater than about 70percent). Those configurations using less compression (about 70 percentor less) had lower performance because their high additive drag featuresoverwhelmed the cowl drag benefit of their lower cowl lip angles.

As shown above, the on-design inlet performance characteristics of therelaxed isentropic compression inlet design showed improvement andvalidation using high fidelity analysis tools. To further validate thefindings of the invention, the off-design characteristics at lowersupersonic Mach number were also analyzed. To address off-designcharacteristics, the 1808 Biconic was evaluated against the 0895Isentropic embodiment of the invention.

FIG. 15 shows a graph plotting CFD based cowl drag coefficient (y-axis)as a function of mass flow ratio at on- and off-design Mach numbers forthe 1808 Biconic inlet and the 0895 Isentropic inlet. Cowl dragcoefficient data for the 1808 Biconic are shown for local flow Machnumbers 1.9, 1.7, and 1.5. Cowl drag coefficient data for the 0895Isentropic are shown for local flow Mach numbers 1.9, 1.7, 1.5, and 1.3.It should be noted that the 0895 Isentropic configuration maintains ancowl drag advantage over the straight-surface inlet throughout the Machranges and mass flow ratio ranges. Although not shown in the Figures, amodest improvement in off-design additive drag was also noted for the0895 Isentropic over the 1808 Biconic.

Finally, an intensive, CFD-based analysis was performed on embodimentsof the relaxed isentropic compression inlet design integrated with arepresentative supersonic study aircraft. The results were compared to a(baseline) conventional straight-surface inlet integrated with the studyaircraft. The integrated inlet analysis was used to determine the effectof the relaxed isentropic compression inlet on sonic boom propagation.The sonic boom analysis was accomplished by integrating the conventionaland relaxed isentropic compression inlet configurations and analyzingthe results with a combination of CFD and traditional sonic boompropagation methods. For purposes of integration, vehicle drag polarsand angle-of-attack characteristics were generated for the studyaircraft configuration analyzed using Overflow software, a CFDanalytical tool.

Approximately nine million grid points were used to model theconfigurations. Euler methodology was applied to the wing and fuselagesurfaces whereas viscous Navier-Stokes was used to solve for the highlycomplex flowfield within the inlet-nacelle-pylori region. Frictionincrements were applied to the wing-fuselage Euler results to accountfor viscous effects. Overflow-based CFD results were used to capture thefull three-dimensional near-field aerodynamic flowfield about theairplane and to initiate the sonic boom propagation process. Front-endvehicle shape morphing as discussed below was modeled in the retractedposition to reduce the analytical overhead, which did not influence theassessment of the inlet's contribution to the sonic boom groundsignature because the signature shaping provided by the front-endmorphing is largely independent of, and does not alter, the wing andinlet shocks for a non-coalesced shock system. The Overflow CFD gridstructure used for sonic boom near-field analysis includes an additionalgrid block below the airplane to obtain high flowfield resolution to alarger distance from the vehicle.

The near-field symmetry plane pressure signatures extracted from the CFDsolutions were used to initiate the sonic boom propagation using theThomas code, a NASA Ames Research Center developed algorithm forextrapolating near field pressures to determine ground-level sonic boomcharacteristics.

FIG. 16-A, FIG. 16-B, and FIG. 16-C show a top view, a front view, and aside view, respectively, of the study aircraft configuration used foranalysis. The study aircraft is a 100,000 lb gross takeoff weight-classplatform designed for a long-range cruise speed of Mach 1.8. As shown inFIGS. 16-A and 16-C, the vehicle capitalizes extensively on area-volumedistribution improvements resulting from recent progress in low sonicboom morphing techniques. Avoiding the uncertainty and high developmentrisk associated with large-scale laminar flow concepts, theconfiguration employs variable wing sweep (FIG. 16-A shows the wings inboth the extended and swept positions) to assure good performance andhandling qualities at takeoff, approach, and landing. The wing itselfincorporates a subsonic leading edge and retains excellent internalvolume characteristics.

As shown in FIGS. 16-A and 16-C, a morphing technology is incorporatedinto the forward fuselage to provide longitudinal extension forsupersonic flight. This morphing technique is theoretically predicted togreatly reduce the sonic boom impulse by breaking the initial vehicleoverpressure wave into a series of reduced-strength shocklets. Theeffective lengthening of the vehicle also assists in preventing thecoalescence of the shocklets into an undesirable, high-impulse N-waveoverpressure pattern. The inclusion of the morphing technology,described in U.S. Pat. No. 6,698,684 which is hereby incorporated in itsentirety, enables improved fuselage area redistribution for the samepeak boom overpressure target. The new area distribution provides for acabin volume comparable to that of large-cabin corporate jets and amuch-improved aft fuselage volume allowance for empennage design leewayand structural stiffening.

The study aircraft incorporates a two-engine, above-wing, podded nacellearrangement that offers positioning latitude and acoustic benefits. Theabove-wing location is predicted to provide far-field sonic overpressureshielding during supersonic flight as well as reduced airportenvironment noise.

It should be understood that the wing shielding reduces downwardpropagation of a substantial portion of the shock energy produced by theinlet-nacelle at supersonic speed. But while effective in reducing sonicboom strength, the inlet shock interaction with the wing upper surfacealso reduces the aerodynamic performance of the wing and creates avehicle configuration that is particularly sensitive to propulsionsystem integration and inlet shock strength. Therefore, local inletsthat achieve performance improvements through cowl streamlining, such asthe relaxed isentropic compression inlet design of the invention,generate weaker cowl shocks that result in less contribution to overallvehicle sonic boom characteristics and an overall vehicle performancebenefit in that the inlet-airframe shock interaction is reduced.

The actual level of improvements in aircraft performance and sonic boomcharacteristics are dependent on the actual aircraft configuration andflight characteristics. As such, the performance and sonic boom datapresented below indicate a representative level of improvement that canbe obtained through employing relaxed isentropic compression inletshaping on the study aircraft only. Results are compared between twovehicle configurations, one using the conventional baseline 1808 Biconicinlet and the other employing the 0890 Isentropic inlet.

FIG. 17 shows a top view of a CFD based surface pressure solution ofwing and fuselage surfaces at freestream Mach 1.8 with the conventional1808 Biconic inlet shown on the left side of the aircraft and the 0890Isentropic inlet shown on the right side of the aircraft. Due to thesymmetry of the aircraft and the analysis, FIG. 17 is broken in half forsimplicity of presentation and for direct comparison between theintegration of the conventional inlet and the relaxed isentropiccompression inlet. The nacelle surfaces were subsequently removed fromthe image shown in FIG. 17 to permit visualization of the shock-winginteraction underneath the nacelles. It should be noted that the relaxedisentropic compression inlet of the embodiments of the invention reducedthe shock strength as shown in FIG. 17. The lower shock strength alsoresults in a more favorable, aft-riding intersection line with the wingupper surface which is beneficial from the drag perspective.

An improvement in cruise drag for the study aircraft of over 7 percentwas seen when employing integrated inlets using relaxed isentropiccompression. These results indicate that the performance characteristicsof the relaxed isentropic compression inlet design, seen during theisolated analysis effort, may be substantially retained once thenacelles are integrated with an airframe.

FIG. 18 presents far-field sonic boom overpressure solutions of aircraftsonic boom signatures for both the conventional 1808 Biconic inlet onthe study aircraft and the 0890 Isentropic inlet on the study aircraft.FIG. 18 plots pressure change from ambient (y-axis) against time inmilliseconds (x-axis). FIG. 18 compares results for a cruise conditionof 51,000 ft and Mach 1.8. As a result of its weaker shock features,peak aircraft overpressure using the 0890 Isentropic inlet has beenreduced by 9 percent on the forward maxima 1000 and by nearly 16 percenton the aft maxima 1001 when compared to results using 1808 Biconic. Risetime 1002 to the first peak is also delayed by nearly 10 percent.

Although the above analysis includes the use of the aircraftconfiguration shown in FIGS. 16-A, 16-B, and 16-C, it would be apparentto those of skill in the art that relaxed isentropic compression inletdesigns, in accordance with embodiments of the invention, may beemployed on alternative aircraft configurations. Further, the location,arrangement, number, and size of relaxed compression isentropic inletdesigns may be altered in accordance with the embodiments of theinvention without deviating from the scope and spirit of the invention.

The relaxed isentropic compression inlet design increases the designlatitude for lofting the inlet cowling region while permitting controlover other key inlet design parameters such as terminal shock Machnumber, diffuser flow distortion, and total pressure recovery. As shown,reduced cowling surface angles may improve inlet drag and interferencedrag characteristics. The reduced slope of the cowling also lowers thecontribution of the inlet to the overall vehicle sonic boomcharacteristic during supersonic flight and decreases the potential foraerodynamic cross-interference between close-coupled inlets.

The relaxed isentropic compression inlet designs in accordance withembodiments of the invention achieve improvements over the conventionalstraight-surface inlet designs without the use of complicated secondarysystems or variable geometry. However, it is contemplated that theinvention may be combined with other systems, such as inlet bypass flowmethods, bleed air-based boundary layer management systems,aerodynamically tailored centerbody support struts, surfacetreatment-based boundary layer management techniques and methods, orother systems and methods. Likewise, it is contemplated that inlets inaccordance with embodiments of the invention may be combined withvarious propulsion systems including, but not limited to, gas turbine,ramjet, scramjet, or combined cycle.

Again, it should be understood that the relaxed isentropic compressiondesign approach may be applied to any external compression or mixedcompression inlet concept, including axisymmetric, partial conic, andtwo-dimensional intakes. In fact, cowling angles for externalcompression inlets can be reduced to approach those employed bytraditional mixed compression inlets using the embodiments of theinvention, merging the inherent shock stability robustness of externalcompression geometry with the high installed performance of mixedcompression.

The foregoing descriptions of specific embodiments of the invention arepresented for purposes of illustration and description. They are notintended to be exhaustive or to limit the invention to the precise formsdisclosed. Obviously, many modifications and variations are possible inview of the above teachings. While the embodiments were chosen anddescribed in order to best explain the principles of the invention andits practical applications, thereby enabling others skilled in the artto best utilize the invention, various embodiments with variousmodifications as are suited to the particular use are also possible. Thescope of the invention is to be defined only by the claims appendedhereto, and by their equivalents.

1. A method of making a supersonic inlet of a jet powered airplane, saidairplane designed for flight at a specific and pre-determined Machnumber, comprising: providing an inlet comprising a compression ramp andcowl; said cowl having an upstream lip; said compression ramp having anupstream straight compression ramp having an apex, connected downstreamwith a concave surface relative to the flow, said concave surfaceconnected downstream with a straight surface; providing said apex withan angle and positioning said cowl lip such that at said Mach number, aninclined shock wave generated at said apex hits said cowl lip; at saidMach number, said cowl lip producing a terminal shock wave extending tothe compression surface; providing said concave surface with a radius ofconcavity producing successive shocklets; said radius of concavity beinglarger than a radius that at said Mach number would cause said shockletsto focus on said cowl lip; at said Mach number, each of said shockletsintercepting said terminal shock wave at a different location betweensaid cowl lip and said compression surface.
 2. The method of claim 1,further comprising reducing, as a result of the radius of concavity, anangle of the cowl relative to a cowl angle for a conventional cowldesigned to align with the local flow angle when the radius of concavitywould cause said shocklets to focus on said cowl lip at the specific andpre-determined Mach number.
 3. The method of claim 1, wherein providingsaid concave surface comprises providing a concavely curved surfacehaving a contour such that, for a plurality of successive locations inthe downstream direction, a local angle of inclination of said concavelycurved surface is smaller than a corresponding local angle ofinclination on a curved surface having a radius that at said Mach numberwould cause said shocklets to focus on said cowl lip.
 4. The method ofclaim 1, wherein providing said concave surface comprises providing aconcavely curved surface having a continuously increasing radius in anaft direction of the compression ramp.
 5. The method of claim 1, whereinproviding the inlet comprising a compression ramp and cowl comprisesproviding an axisymmetric ramp and providing a circumferential cowlstructure.
 6. The method of claim 1, further comprising configuring saidconcave surface in accordance with at least one of method ofcharacteristics (MOC) and computational fluid dynamics (CFD) techniques.